On Certifying NonUniform Bounds against Adversarial Attacks
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Proceedings of the 36th International Conference on Machine Learning, PMLR 97:40724081, 2019.
Abstract
This work studies the robustness certification problem of neural network models, which aims to find certified adversaryfree regions as large as possible around data points. In contrast to the existing approaches that seek regions bounded uniformly along all input features, we consider nonuniform bounds and use it to study the decision boundary of neural network models. We formulate our target as an optimization problem with nonlinear constraints. Then, a framework applicable for general feedforward neural networks is proposed to bound the output logits so that the relaxed problem can be solved by the augmented Lagrangian method. Our experiments show the nonuniform bounds have larger volumes than uniform ones. Compared with normal models, the robust models have even larger nonuniform bounds and better interpretability. Further, the geometric similarity of the nonuniform bounds gives a quantitative, dataagnostic metric of input featuresâ€™ robustness.
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